Question Determine if the solution to $2 \cdot x=6$ , $-2 \cdot x=6.1$ , $2.9 \cdot x=-6.04$ , or $-2.473 \cdot x=-6.859$ is positive or negative.

Studdy Solution

STEP 1

Assumptions
1. We are given four separate equations.
2. We need to determine the sign (positive or negative) of the solution for each equation.
3. The equations are linear, with a single variable $x$ .

STEP 2

For equation a, $2 \cdot x = 6$ , we will solve for $x$ to determine the sign of the solution.
$x = \frac{6}{2}$

STEP 3

Calculate the value of $x$ for equation a.
$x = \frac{6}{2} = 3$

STEP 4

Since $3$ is a positive number, the solution for equation a is positive.

STEP 5

For equation b, $-2 \cdot x = 6.1$ , we will solve for $x$ to determine the sign of the solution.
$x = \frac{6.1}{-2}$

STEP 6

Calculate the value of $x$ for equation b.
$x = \frac{6.1}{-2} = -3.05$

STEP 7

Since $-3.05$ is a negative number, the solution for equation b is negative.

STEP 8

For equation c, $2.9 \cdot x = -6.04$ , we will solve for $x$ to determine the sign of the solution.
$x = \frac{-6.04}{2.9}$

STEP 9

Calculate the value of $x$ for equation c.
$x = \frac{-6.04}{2.9} \approx -2.08276$

STEP 10

Since $-2.08276$ is a negative number, the solution for equation c is negative.

STEP 11

For equation d, $-2.473 \cdot x = -6.859$ , we will solve for $x$ to determine the sign of the solution.
$x = \frac{-6.859}{-2.473}$

STEP 12

Calculate the value of $x$ for equation d.
$x = \frac{-6.859}{-2.473} \approx 2.77433$

STEP 13

Since $2.77433$ is a positive number, the solution for equation d is positive.
The solutions are as follows: a. Positive b. Negative c. Negative d. Positive

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Question Determine if the solution to $2 \cdot x=6$ , $-2 \cdot x=6.1$ , $2.9 \cdot x=-6.04$ , or $-2.473 \cdot x=-6.859$ is positive or negative.

Studdy Solution

STEP 1

Assumptions
1. We are given four separate equations.
2. We need to determine the sign (positive or negative) of the solution for each equation.
3. The equations are linear, with a single variable $x$ .

STEP 2

For equation a, $2 \cdot x = 6$ , we will solve for $x$ to determine the sign of the solution.
$x = \frac{6}{2}$

STEP 3

Calculate the value of $x$ for equation a.
$x = \frac{6}{2} = 3$

STEP 4

Since $3$ is a positive number, the solution for equation a is positive.

STEP 5

For equation b, $-2 \cdot x = 6.1$ , we will solve for $x$ to determine the sign of the solution.
$x = \frac{6.1}{-2}$

STEP 6

Calculate the value of $x$ for equation b.
$x = \frac{6.1}{-2} = -3.05$

STEP 7

Since $-3.05$ is a negative number, the solution for equation b is negative.

STEP 8

For equation c, $2.9 \cdot x = -6.04$ , we will solve for $x$ to determine the sign of the solution.
$x = \frac{-6.04}{2.9}$

STEP 9

Calculate the value of $x$ for equation c.
$x = \frac{-6.04}{2.9} \approx -2.08276$

STEP 10

Since $-2.08276$ is a negative number, the solution for equation c is negative.

STEP 11

For equation d, $-2.473 \cdot x = -6.859$ , we will solve for $x$ to determine the sign of the solution.
$x = \frac{-6.859}{-2.473}$

STEP 12

Calculate the value of $x$ for equation d.
$x = \frac{-6.859}{-2.473} \approx 2.77433$

STEP 13

Since $2.77433$ is a positive number, the solution for equation d is positive.
The solutions are as follows: a. Positive b. Negative c. Negative d. Positive

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Question Determine if the solution to 2⋅x=62 \cdot x=62⋅x=6, −2⋅x=6.1-2 \cdot x=6.1−2⋅x=6.1, 2.9⋅x=−6.042.9 \cdot x=-6.042.9⋅x=−6.04, or −2.473⋅x=−6.859-2.473 \cdot x=-6.859−2.473⋅x=−6.859 is positive or negative.

Studdy Solution

STEP 1

Assumptions1. We are given four separate equations.2. We need to determine the sign (positive or negative) of the solution for each equation.3. The equations are linear, with a single variable xxx.

STEP 2

For equation a, 2⋅x=62 \cdot x = 62⋅x=6, we will solve for xxx to determine the sign of the solution.x=62x = \frac{6}{2}x=26​

STEP 3

Calculate the value of xxx for equation a.x=62=3x = \frac{6}{2} = 3x=26​=3

STEP 4

Since 333 is a positive number, the solution for equation a is positive.

STEP 5

For equation b, −2⋅x=6.1-2 \cdot x = 6.1−2⋅x=6.1, we will solve for xxx to determine the sign of the solution.x=6.1−2x = \frac{6.1}{-2}x=−26.1​

STEP 6

Calculate the value of xxx for equation b.x=6.1−2=−3.05x = \frac{6.1}{-2} = -3.05x=−26.1​=−3.05

STEP 7

Since −3.05-3.05−3.05 is a negative number, the solution for equation b is negative.

STEP 8

For equation c, 2.9⋅x=−6.042.9 \cdot x = -6.042.9⋅x=−6.04, we will solve for xxx to determine the sign of the solution.x=−6.042.9x = \frac{-6.04}{2.9}x=2.9−6.04​

STEP 9

Calculate the value of xxx for equation c.x=−6.042.9≈−2.08276x = \frac{-6.04}{2.9} \approx -2.08276x=2.9−6.04​≈−2.08276

STEP 10

Since −2.08276-2.08276−2.08276 is a negative number, the solution for equation c is negative.

STEP 11

For equation d, −2.473⋅x=−6.859-2.473 \cdot x = -6.859−2.473⋅x=−6.859, we will solve for xxx to determine the sign of the solution.x=−6.859−2.473x = \frac{-6.859}{-2.473}x=−2.473−6.859​

STEP 12

Calculate the value of xxx for equation d.x=−6.859−2.473≈2.77433x = \frac{-6.859}{-2.473} \approx 2.77433x=−2.473−6.859​≈2.77433

STEP 13

Since 2.774332.774332.77433 is a positive number, the solution for equation d is positive.The solutions are as follows: a. Positive b. Negative c. Negative d. Positive

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Question Determine if the solution to $2 \cdot x=6$ , $-2 \cdot x=6.1$ , $2.9 \cdot x=-6.04$ , or $-2.473 \cdot x=-6.859$ is positive or negative.

Assumptions
1. We are given four separate equations.
2. We need to determine the sign (positive or negative) of the solution for each equation.
3. The equations are linear, with a single variable $x$ .

For equation a, $2 \cdot x = 6$ , we will solve for $x$ to determine the sign of the solution.
$x = \frac{6}{2}$

Calculate the value of $x$ for equation a.
$x = \frac{6}{2} = 3$

Since $3$ is a positive number, the solution for equation a is positive.

For equation b, $-2 \cdot x = 6.1$ , we will solve for $x$ to determine the sign of the solution.
$x = \frac{6.1}{-2}$

Calculate the value of $x$ for equation b.
$x = \frac{6.1}{-2} = -3.05$

Since $-3.05$ is a negative number, the solution for equation b is negative.

For equation c, $2.9 \cdot x = -6.04$ , we will solve for $x$ to determine the sign of the solution.
$x = \frac{-6.04}{2.9}$

Calculate the value of $x$ for equation c.
$x = \frac{-6.04}{2.9} \approx -2.08276$

Since $-2.08276$ is a negative number, the solution for equation c is negative.

For equation d, $-2.473 \cdot x = -6.859$ , we will solve for $x$ to determine the sign of the solution.
$x = \frac{-6.859}{-2.473}$

Calculate the value of $x$ for equation d.
$x = \frac{-6.859}{-2.473} \approx 2.77433$

Since $2.77433$ is a positive number, the solution for equation d is positive.
The solutions are as follows: a. Positive b. Negative c. Negative d. Positive